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Recover a number (Posted on 2019-10-29) Difficulty: 2 of 5
A certain positive integer N is twice the product of its digits.

Find N.

See The Solution Submitted by Ady TZIDON    
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computer solution | Comment 1 of 3

Note - one need only search numbers up to n digits, where 

2 x 9^n > 10^n  

So n is less than or equal to 6. After that the equality is impossible since  at n=7, 10^ 7 > 2 * 9*9*9*9*9*9*9    

        program pu

        implicit none

        integer i,j,dum,prod,top,dig

           do i = 1, 10**7

           prod=1

           dum=i

                top=log10(1.*i)

                do j=top,0,-1

                dig=dum*10.**(-j)

                prod=prod*dig

                dum=dum-dig*10**j

                enddo

           if(2*prod.eq.i)print*,i

           enddo

        end

rabbit-3:~ lord$ pu

          36

rabbit-3:~ lord$

Edited on October 29, 2019, 11:52 am
  Posted by Steven Lord on 2019-10-29 09:57:33

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